Toronto Math Forum

In addition to Part c solution I posted above, here is Problem 2 Part d Bonus solution to prove eigenvalues are simple.

Thanks for a and b. As no one has posted Problem 2 part c yet, I just did using IBP as attached.

Thanks Aida for posting Part b in December. As there is still NO solution posted for Part d yet, I spent 1 hour to write part d and post attached same 2 images, first by camera, second by scan.

Thanks professor. Here I used error function in the textbook, instead of that given in the homework, but yes they are same. In part d, I got limit u(x,t)=1 for Neumann condition.

http://www.math.toronto.edu/courses/apm346h1/20129/HA9.html#problem-9.3


Problem 3a Dirichlet Solution Attached

Yes--fixed now in html (not in pdf)

Thanks for fixing Problem 2. Solution Attached.

Thanks Calvin's solutions at 21:47, especially parts c and d bonus, which are not required. I only posted parts a and b at 21:32, which are all required work for Problem 1. By the way, note in my part b, r should be replaced by ρ. Part a posted t 21:31 is OK.

Problem 3 b my own solution attached for 2 counter examples, different from Calvin's solution, I just typed it in Paint thanks!